## Graduate Faculty and Their Research

**Alexander Goncharov [1]**,

**Ph.D., (USSR). European Mathematical Society Prize.**Arithmetic Algebraic Geometry: polylogarithms, zeta-functions, periods, Hodge theory, motives, motivic Galois groups, Quantum geometry of moduli spaces, Representation Theory and Mathematical Physics

**Students:**

**Andrew Casson [2]**,

**Cambridge University, 1969. Royal Society Fellow.**Low-dimensional topology, four manifold theory, algebraic topology, hyperbolic geometry.

**Gregory Margulis [3]**,

**Ph.D., Moscow, 1970. American Academy of Arts and Sciences. National Academy of Sciences. Fields Medal.**Lie group theory, ergodic theory, number theory, network theory, and dynamics.

**Students:**

**Gregg Zuckerman [5]**,

**Ph.D., Princeton, 1975.**Representation theory, applications of Lie theory, mathematical physics.

**Hee Oh [6]**,

**Ph.D., Yale, 1997. Satter Prize.**Homogeneous dynamics, discrete subgroups of Lie groups, Kleinian groups, hyperbolic geometry, and the resulting applications of number theory.

**Students:**

**Igor Frenkel [7]**,

**Ph.D., Yale, 1980. American Academy of Arts and Sciences.**Infinite-dimensional algebras, representation theory, applications of Lie theory, mathematical physics.

**Students:**

**Peter Jones [8]**,

**Ph.D., UCLA, 1978. American Academy of Arts and Sciences. National Academy of Sciences. Salem Prize.**Real, complex, and Fourier analysis, singular integrals, potential theory, dynamical systems.

**Ronald Coifman [9]**,

**Ph.D., Geneva, 1965. Philips Professor of Mathematics, National Academy of Sciences, American Academy of Arts and Sciences, National Medal of Science, Rolf Schock prize .**Nonlinear analysis, Scattering theory, Real and complex analysis, Singular integrals, Numerical analysis, Harmonic analysis and Geometry in high dimension Data Analysis

**Students:**

**Stefan Steinerberger [10]**,

**Ph.D., Bonn, 2013.**Real, Complex and Harmonic Analysis, Spectral Theory, Partial Differential Equations, Analytic Number Theory and Applications.

**Students:**

**Van Vu [11]**,

**Ph.D., Yale, 1998. Polya Prize. Fulkerson Prize.**Combinatorics, probability, additive number theory, data science.

**Students:**

**Vladimir Rokhlin [13]**,

**Ph.D., Rice, 1983. National Academy of Sciences.**Numerical scattering theory, elliptic partial differential equations, numerical solution of integral equations.

**Wilhelm Schlag [14]**,

**Ph.D., Caltech 1996.**Spectral Theory, Partial differential evolution equations, harmonic analysis

**Yair Minsky [15]**,

**Ph.D., Princeton University, 1989.**Kleinian groups, Teichmuller theory, geometric group theory, holomorphic dynamics, differential geometry.

**Students:**

**Yifeng Liu [18]**,

**Ph.D., Columbia University, 2012.**Algebraic number theory, algebraic and arithmetic geometry, automorphic forms

**Students:**